It is known that there are only 14 reasonable tensor norms in $Ban$. On the other hand it is well known fact for topologists that one can obtain only 14 different sets from a given set applying closure and complementation operations.

It seems like a pure coincidence but... both constructions starts with the single object (a set/ the injective tensor norm), then apply only predescribed operations (closure and complement/ transpose, dual and right projective associate) and get only 14 different objects in the end.

Is this a simple coincidence or there is something deep behind the scenes? Maybe someone knows other examples?